Point u is on line segment tv given tv = x + 10, tu =3x-8, and Uv = 10 determine the numerical length of tv

Answer:

726 children

242 adults

Step-by-step explanation:

a + c = 968

6c + 11a = 7018

Use Substitution:  c = 968-a

6(968-a) + 11a = 7018

5808 - 6a + 11a = 7018

5a = 1210

a = 242

c = 968 - 242 = 726

The true statements are:

There are 56 fluid ounces of milk left.

There is more than 1 / 4 gallon of milk left.

What are the true statements?

The first step is to convert gallons to cups.

1 cup = 16 gallons

Then, convert quarts to cups

1 quart = 4 cups

1 1/2 x 4

3/2 x 4 = 6 cups

Total cups left = 16 - 6 - 3 = 7 cups

1 cup = 8 ounces

Total milk left in ounces: 8 x 7 = 56 ounces

1 cup = 1/16 gallons

Total milk left in gallons: 1 / 16 x 7 = 7/16  gallons

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4Step-by-step explanation:

Answer:

Step-by-step explanation:

Any solid dot choices are incorrect. The end point is not included in the answer.  I don't see any solid dots, so that eliminates nothing.

4x>-8                       Divide by 4

4x/4 > - 8/4             Simplify

x > - 2

What this tells us is that x must be greater than - 2

You have to be going RIGHT.

So the answer is 3

The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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Answer:

\(\angle CAD = 20^\circ\)

Step-by-step explanation:

Given

\(\angle CBD = 20^\circ\)

Required

Determine the measure of \(\angle CAD\)

To calculate CAD, we have:

\(\angle CAD = \angle CBD\) --- angle in the same segment

Hence:

\(\angle CAD = 20^\circ\)

Answer:

a

Step-by-step explanation:

15*20%=3

15-3=12

Answer: 5

Step-by-step explanation:

The greatest common factor of 15c^2 and 25n is 5 because if you divid the two numbers by 5, they will both be in their primal state.

15c^2 / 5 = 3c^2

25n / 5 = 5n

Answer:

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) P(X = 3) = 0.2541.

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is 0.5518.

Step-by-step explanation:

We are given that in a school it is found that 30% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let X represent the number who do not work during summer vacation.

Let X = the number of adults who do not work during summer vacation

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) The above situation can be represented through binomial distribution;

\(P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......\)

where, n = number of trials (samples) taken = 8 adults

            r = number of success = exactly three

            p = probability of success which in our question is % of adults who

                  do not work at all while on summer vacation, i.e; p = 0.25

SO, X ~ Binom(n = 8, p = 0.30)

Now, the probability that exactly 3 adults do not work at all while on summer vacation is given by = P(X = 3)

          P(X = 3) =  \(\binom{8}{3}\times 0.30^{3} \times (1-0.30)^{8-3}\)

                        =  \(56 \times 0.30^{3} \times 0.70^{5}\)

                        =  0.2541

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is given by = P(X \(\leq\) 2)

      P(X \(\leq\) 2) = P(X = 0) + P(X = 1) + P(X = 2)

= \(\binom{8}{0}\times 0.30^{0} \times (1-0.30)^{8-0}+\binom{8}{1}\times 0.30^{1} \times (1-0.30)^{8-1}+\binom{8}{2}\times 0.30^{2} \times (1-0.30)^{8-2}\)

= \(1 \times 0.30^{0} \times 0.70^{8}+8 \times 0.30^{1} \times 0.70^{7}+28\times 0.30^{2} \times 0.70^{6}\)

= 0.5518

Answer:

#9 = 24

#19 = -33

Step-by-step explanation:

Answer:

(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:

FV = P * ((1 + r)^n - 1) / r) * (1 + r)

where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.

In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:

FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)

FV ≈ €743,704.96

Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.

(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:

PV = P * ((1 - (1 + r)^(-n)) / r)

where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.

In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:

PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)

P ≈ €22,630.53

Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.

(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).

Total deposits = €22,630.53 * 30 = €678,915.90

Total withdrawals = €25,000 * 20 = €500,000

Initial balance = €743,704.96

Total interest earned = Total withdrawals - Total deposits - Initial balance

Total interest earned = €500,000 - €678,915.90 - €743,704.96

Total interest earned ≈ -€922,620.86

Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.

Step-by-step explanation:

Answer:

10000

Step-by-step explanation:

Answer:

there are 1000000 possible 6 digit pin numbers

Step-by-step explanation:

one way to think about this is it can be any number from 000000 to 999999.

the reason the answer is 1000000 and not 999999 is because 000000 is also a valid pin number.

sorry if this is confusing!

Answer:

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 500

sample proportion

                \(p = \frac{x}{n} = \frac{60}{500} = 0.12\)

Level of significance ∝= 0.90 or 0.10

90% confidence interval for the true proportion of men who applied to the nursing   program.​

\((p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })\)

\((p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })\)

\((0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })\)

On calculation , we get

( 0.12 - 0.02326 , 0.12 + 0.02326)

(0.09674 ,0.14326)

Final answer:-

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Answer:

24

Step-by-step explanation:

a^2+b^2=c^2

10^2+b^2=26^2

100+b^2=676

b^2=576

b=24

Answer:

Domain: x \(\geq\) -5

Range: y \(\geq\) -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

The equation is given as:

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000

From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)

So, we start by multiplying 2 and 4

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000

Add 8 and 48000

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000

Divide 48008 by 8

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000

Subtract 1 from 6001

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000

Multiply 6000 and 30

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000

Multiply 180000 by 2

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000

Evaluate the sum

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000

Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

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Answer:

The magnitude of vector is:

\(\left|\begin{pmatrix}5&-6\end{pmatrix}\right|=\sqrt{61}\)

v = <5, -6> means the vector has x-coordinate x = 5 and y-coordinate y = -6, so the vector v = <5, -6>  is heading towards SE.

Thus, option ( j ) is correct.

i.e.  \(\sqrt{61},\:SE\)

Step-by-step explanation:

Given the vector

v = <5, -6>

Determining the magnitude of the vector

To find a magnitude of a vector v = (a, b) we use the formula

\(||v||\:=\:\sqrt{a^2+b^2}\)

Magnitude of the vector is basically termed as the length of the vector, which is denoted by

\(|\left(5,\:-6\right)|=\sqrt{\left(5\right)^2+\left(-6\right)^2}\)

            \(=\sqrt{5^2+6^2}\)

             \(=\sqrt{25+36}\)

             \(=\sqrt{61}\)

Thus, the magnitude of vector is:

\(\left|\begin{pmatrix}5&-6\end{pmatrix}\right|=\sqrt{61}\)

As the vector v = <5, -6> lies in 4th quadrant.

v = <5, -6> means the vector has x-coordinate x = 5 and y-coordinate y = -6, so the vector v = <5, -6>  is heading towards SE.

Thus, option ( j ) is correct.

i.e.  \(\sqrt{61},\:SE\)

We will deterine the averate rate of change between 2001 and 2002 as follows:

So, the average rate of change was 9 millions,

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

Answer:

2

Step-by-step explanation:

“PEMDAS” is parenthesis, exponents, multiplication, division, addition, subtraction

\(\frac{1}{2}(4*5) - 2^{3}\)

parenthesis: would be (4*5) = 20

exponents: 2³ = 2 x 2 x 2 = 8

\(\frac{1}{2}(20) - 8\)

multiplication: \(\frac{1}{2}(20)\) = 10 as half (0.5) of 20 is 10

subtraction: 10 - 8 = 2

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Answer:

10

Step-by-step explanation:

Total Ratio =1 1/2 +2 +1/2

=2+2

=4

=40÷4

=10

=

The volume of the sphere is 523.333 cu. In., and when rounded to the nearest thousandth, the answer is 523.333 cu. In.

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. In this case, the diameter of the sphere is 10 inches, so we can calculate the radius by dividing the diameter by two. This gives us a radius of 5 inches. Plugging these values into the formula, we get V = (4/3)π(5)³ = 523.333 cu. In. Therefore, the volume of the sphere is 523.333 cu. In., and when rounded to the nearest thousandth, the answer is 523.333 cu. In.

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On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

Answer:no idea

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

The answer is 1628. Because 16 x 21 = 28 x 12 = 336

Hope this helps

Answer:

D. 5.5 miles

Explanation:

The time taken by both siblings = Half an hour = 0.5 hour

The brother walks away at a speed of 3.5 miles per hour. The distance covered by the brother in half an hour:

The sister runs at a speed of 7.5 miles per hour. The distance covered by the sister in half an hour:

Since they are moving in opposite directions, the distance between them will be the sum of the distances in each direction.

The siblings are 5.5 miles apart after half an hour.